Abstract
Accurate estimations of reference evapotranspiration (ETref) are extremely important for maximizing the beneficial use of water and hydrologic applications, particularly in arid and semiarid regions where water sources are so limited. The aim of this study is to develop mathematical models to calculate the daily ETref using a gene expression programming (GEP) technique. Eight GEP models (GEP-MOD1-8) were developed from combinations of climatic variables. The Penman-Monteith equation was considered the reference method, with the reference plant height varying from 5 to 105 cm in 5-cm increments. Daily climatic variables collected from 13 meteorological stations, one station from every region within the Kingdom of Saudi Arabia, covered the 1980 to 2010 period. Of the available climatic data, 65 % was used in the training process for the eight developed GEP models, and 35 % was used in the testing process. The accuracy of the eight developed GEP models to estimate ETref varied in significance depending on the climatic variables that were included. As more climatic parameters were input, the accuracy of the GEP model increased. For the testing process, the coefficient of determination (R-2) ranged from a low of 63.4 % for GEP-MOD1 to a high of 95.4 % for GEP-MOD8, and the root mean square error (RMSE) values ranged from 3.19 mm day(-1) for GEP-MOD1 to 1.14 mm day(-1) for GEP-MOD8. From the spatial evaluation, the values of RMSE ranged from 3.27 mm day(-1) for GEP-MOD1 to 1.21 mm day(-1) for GEP-MOD8. In addition, the respective RMSE values resulting from GEP-MOD8 for plant heights of 50 and 12 cm were 0.75 and 0.96 cm. This implies that the developed GEP-MOD8 can be used for any value of the reference plant height ranging from 5 to 105 cm with insignificant errors. Interestingly, solar radiation had an almost insignificant effect on ETref in the hyper-arid conditions. In contrast, wind speed and plant height had a large positive effect on increasing the accuracy of calculating ETref.